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Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics

Journal Article · · Journal of Computational Physics
 [1];  [1];  [2];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Davis, CA (United States)
+ Show Author Affiliations

n this paper, we introduce a multigrid block-based preconditioner for solving linear systems arising from a Discontinuous Galerkin discretization of the all-speed Navier-Stokes equations with phase change. The equations are discretized in conservative form with a reconstructed Discontinuous Galerkin (rDG) method and integrated with fully-implicit time discretization schemes. To robustly converge the numerically stiff systems, we use the Newton-Krylov framework with a primitive-variable formulation (pressure, velocity, and temperature), which is better conditioned than the conservative-variable form at low-Mach number. In the limit of large acoustic CFL number and viscous Fourier number, there is a strong coupling between the velocity-pressure system and the linear systems become non-diagonally dominant. To effectively solve these ill-conditioned systems, an approximate block factorization preconditioner is developed, which uses the Schur complement to reduce a 3 x 3 block system into a sequence of two 2 x 2 block systems: velocity-pressure,vP, and velocity-temperature, vT. We compare the performance of the vP-vT Schur complement preconditioner to classic preconditioning strategies: monolithic algebraic multigrid (AMG), element-block SOR, and primitive variable block Gauss-Seidel. The performance of the preconditioned solver is investigated in the limit of large CFL and Fourier numbers for low-Mach lid-driven cavity flow, Rayleigh-Bénard melt convection, compressible internally heated convection, and 3D laser-induced melt pool flow. Here, numerical results demonstrate that the vP-vT Schur complement preconditioned solver scales well both algorithmically and in parallel, and is robust for highly ill-conditioned systems, for all tested rDG discretization schemes (up to 4th-order).

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1577941
Alternate ID(s):
OSTI ID: 1701812
Report Number(s):
LLNL-JRNL--745515; 900481
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 397; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (1)

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics journal November 2018

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97 MATHEMATICS AND COMPUTING
All speed fluid dynamics
Block preconditioning
Fully implicit
Newton Krylov
Physics-based preconditioning
Reconstructed discontinuous Galerkin method